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# 182Exam1-Review-Spring2011-ANSWERS - REVIEW FOR MATH 182...

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Unformatted text preview: REVIEW FOR MATH 182 Exam 1 Spring 2011 ﬁrm 5 WW1 M . 5 1 1.E'1" h ' Xptmw 5'11, m do: is an "improper integral“ Evaluate it if it converges. If it diverges show why. ymPWMJV- hﬁiamﬁw '_:'%%m'lqm 1... Qu/Etamtie3 @Mwéngff W \ii 10 3. Evaluate [0G {2 :3 +1 1W (£2: [email protected] If it diverges, show why . 4 1 . 1 t 4. After a 1.1111 the method of substitution to / -———-— dt, the inte 1211 becomes: pp } g Wig + 1 g l 1 1 1 3 1 1 1 {séfuedu (mi/amen {ezfuvdu 0 1 O . Evaluate / 11... 2 1 01.1: if it converges. If at d1ve1ges,?show why. 5 \$"‘ 1 00 1 (e)4/ 1130511 0 3 5. Write 2113- without sigma notation. 1:0 4 n :‘l E + I} I F" 1-“— § LEW; -, , 13.491111” 1 2' v3 3 1 1 1 1 (f) 4/ u"? (in (g) —/ ui du 1 4 1) £10 «1—121! 11111423.? 5313 5. Write EU. + k2) without sigma notation and circle the correct vaiue below. kmD (a) 15 3 7. Write :(w i=0 (b) 34 (e) 30 (d) 28 (f) 38 (g) none of these 1)j_12j without sigma notation and circle the correct value below. {a} —5 (b) 5 (c) 15 (d) —6 (e) “15 (f) “~14 (g) none of these 8‘ Express lEI'DlIEn 0 Z J5; A5121: as a deﬁnite integrai Where P is a partition of [1, 3]. WM k= _ *1“ f [- 1 m :12“ A 9. Express 17%" 0 Z 1 w ck sin{ck) A331; as a deﬁnite integrai where 13 is a partition of [0, 7r]. wwﬁmm. ' —' k=1 10. Fmd the average value of f(\$) : :5 on [71, 3]. Please Show yam" work. ...., 7" w 3; ‘2‘ w! 11. If/1 f (m) (17:17— 30 then the average value of f on [1 Allis /O 2 12. I wrote / y (ﬂy : 9;)— on my test and got docked a point. Why? 31’ ﬁgfﬁ . .. Wé’ M 5%? hi +. C. i3. EVe’iUete‘the foilowing integrals. Circle tile correct answer and please Show you?" work. Just circling an answer wili not receive credit on the (32am, unless work 2's shown! In particular, when substitution is called for, the process must \$9751.42 K4“? J, £1,wa be shown. (a)%x%(5 +3x)+0 ‘ (b) §(m+1)%(2+3m)+0 :F-(a:+1)%(3rr-—'2)+C (d) %22(2+1)% +0 (e)‘— (2+1)% +0 ' (f) %\$% (—5+3;U) +0- I (g) none ofthese- (b) f%dy (3)%9%T%y%+0 (b)—§-3y2+2\/ﬁ+0 (0)2y4%_%y"%+0 (d) %y% + éﬂ+ C' (e) §y% a” %y% + 0 @§ ﬁ-k 2f+0 (g) none ofthese ﬂ 2 a, F 7' W 2%? (c)/t4:11dt MM”‘£:+HA~C§[M“ “A: 1 @ (111(3) 4mm) (23) —in(2 )+§1n(3) ((3) mg in(2)+in(3) (e) w~21w(in(3)+in(2)) (e) 315 (1n(3) + in (2)) (f ) ~11} (3) + 111(2 ) (g) none of these (d) [#:3211018 (a) gsugggw a) gate :0 (c) 58 +11522WWWQ93§M8 +11” (e) %32 + \$4134 + O (f) 3in(s + HMO W WM WWW} :0: none of these {:Mjo . z Wksu 3&1 idmél/ " H (6) [ re” d?“ iv? M, =3 V11, ﬂaw-2221i!“ “WWWMMELWW 2 S?“ «m we WW, me ”M? (a) 2eT2 + 0 6T3 + C (c) éeg’" 1’“ C (d) r3 a?“ + C (e) e27“ + O {f} T2 e?"3 + G (g) none of these 2 3 3 14. If / ﬁt) at z 2 and / ﬁt) at 2: 7 then / ﬁt) dram f ' . 2 151 Find m/ x/2t3+1.dt #2}; W W 9‘ 2 16. Find ix e”2 du. :: a we 6, W (in 2 J}? 1?. Estimate [3 1 —— 3:2 d2 in three ways: (a) using alieft endpoint Riemann sum with 4 subinterveis, W Li": - 3' 5” (b) using a right endpoint Riemann sum with 4 su'bintervais and _... t?“ a; SW, (C) using a midpoint Riemann sun: with 4 subint‘ervals. H C (a 2 S” R 18 AsSume that you knew the function Values {mm the given table Estimate [4 f(m))dx1e three ways: (a) using a ieft endpoint Riemann sum with 6 snbintervals, 2“ “Z 3» {b} using a right endpoint Riemann sum with 5 subintervals and 3 l .2. 3 (C) using a midpoint Riemann sum With 3 snbintervals. 2- 0 2 19. {3.) Find the values of 93 Where the graphs of the curves y 2 a: w 9: and y - a: + 3 intersect, ”showing your work using algebra. 1.” ylwzx-HBﬂ- <3 Q n+3)” er.) we (h) Sketch a picture of the region bouncied between the curves in part (a) (c ) Find the area of the region in part0) [-3 ”if—+2; m (5452” 351%: ...—. l 20. The graphs of the curves y : .222 —2:27 and y x 2—2: are shown. Which integrai gives the area between them?2 f2 (a)/02\$2~mw2dsc( \$+2m\$2 do: (c}/21332—x—2dm @ZZ m—i—Q—xz d1 (e)/: 332+m+2d93 (f) [—3 xgmarmﬁda: 1 21. Sketch a picture of the region bounded between the curve :1} 2 x3 4:132 w 29: and the zen—axis. Find the area (if this region. 2-2;. Using the graphs below1 write the letter of the correct graph in the blank corresponding to each of these: :(i) Left- endpein't Riemann sum .1 (iii) Right endpoint Riemalin sum .-.__ (v) Lower Riemann sum E (iii) Midpoint Riemann sum .9:— (iv) Upper Riemann sum .1; ...
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